Question

# When a stationary wave is formed, then its frequency is

A
Same as that of the individual waves
B
Twice that of the individual waves
C
Half that of the individual waves
D
That of the individual waves

Solution

## The correct option is A Same as that of the individual wavesLet us consider a progressive wave of amplitude $$a$$ , wavelength $$\lambda$$ and frequency $$f=\dfrac { 1 }{ T }$$ travelling in the direction of $$X$$- axis whose equation is given by-$${ y }_{ 1 }=a\sin { (2\pi [\dfrac { t }{ T } -\dfrac { x }{ \lambda } ] } )$$This wave is reflected from a free end and it travels in the negative direction of $$X$$- axis with frequency $$f=\dfrac { 1 }{ T }$$$${ y }_{ 1 }=a\sin { (2\pi [\dfrac { t }{ T } +\dfrac { x }{ \lambda } ] } )$$According to principle of superposition$$\Rightarrow { y }_{ 1 }+{ y }_{ 2 }=a\sin { (2\pi [\dfrac { t }{ T } -\dfrac { x }{ \lambda } ] } )+a\sin { (2\pi [\dfrac { t }{ T } +\dfrac { x }{ \lambda } ] } )$$$$\Rightarrow { y }_{ 1 }+{ y }_{ 2 }=a\sin { \left( \dfrac { 2\pi t }{ T } \right) } \cos { \left( \dfrac { 2\pi x }{ \lambda } \right) }$$Here we can see the frequency of resultant wave is also $$f=\dfrac { 1 }{ T }$$.Physics

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